In recent years, two independent research fields, i.e. non-Hermitian andstrongly correlated systems have been merged, forming an important researchfield in physics. The progress of relevant theories and experiments hasreshaped our understanding of matter. In this field, the research object isnot limited to the influence of non-Hermiticity on the energy spectrum andthe eigenstate properties of many-body systems. Researchers have paid more attentionto the manipulation of quantum states. It is universally received that the exceptional point is the most significant featurethat distinguishes non-Hermitian quantum mechanics from Hermitian quantum mechanics. In addition to the recent advances in non-Hermitian topological band theory and quantum sensing around the exceptional points, this paper concentrates on the non-Hermitian critical dynamical phenomenon and its application to the quantum many-body system. When the system has an exceptional point, an arbitrary initial state belonging to the coalescent subspace will be projected on the coalescent state. Based on the directionality of the evolved quantum state, this paper reviews our several representative researches in recent years, including local-field-induced dynamical magnetization, quantum phase transition in transverse field, Ising model at non-zero temperature, quantum mold casting in the center-environment system, as well as superconducting state preparation in the non-Hermitian strongly correlated system. We also focus on the new preparation methods and detection schemes of non-equilibrium quantum states related to exception points.
In recent years, two independent research fields, i.e. non-Hermitian andstrongly correlated systems have been merged, forming an important researchfield in physics. The progress of relevant theories and experiments hasreshaped our understanding of matter. In this field, the research object isnot limited to the influence of non-Hermiticity on the energy spectrum andthe eigenstate properties of many-body systems. Researchers have paid more attentionto the manipulation of quantum states. It is universally received that the exceptional point is the most significant featurethat distinguishes non-Hermitian quantum mechanics from Hermitian quantum mechanics. In addition to the recent advances in non-Hermitian topological band theory and quantum sensing around the exceptional points, this paper concentrates on the non-Hermitian critical dynamical phenomenon and its application to the quantum many-body system. When the system has an exceptional point, an arbitrary initial state belonging to the coalescent subspace will be projected on the coalescent state. Based on the directionality of the evolved quantum state, this paper reviews our several representative researches in recent years, including local-field-induced dynamical magnetization, quantum phase transition in transverse field, Ising model at non-zero temperature, quantum mold casting in the center-environment system, as well as superconducting state preparation in the non-Hermitian strongly correlated system. We also focus on the new preparation methods and detection schemes of non-equilibrium quantum states related to exception points.
The study of quantum criticality has historically been confined to Hermitian systems, where closed-system approximations neglect environmental interactions. However, a significant portion of quantum phenomena occurs in open systems, necessitating a departure from this conventional framework. This paper explores non-Hermitian quantum criticality in open many-body systems, delving into the unique phases and phase transitions that emerge due to dissipation, gain, and other non-conservative interactions. We establish a comprehensive framework that integrates concepts from biorthogonal quantum mechanics, Liouvillian dynamics, and tensor network methods to characterize critical phenomena, including dynamical quantum phase transitions and the emergence of non-Hermitian quantum many-body scars. Through an extensive literature review, we highlight how the interplay of non-Hermiticity with many-body correlations leads to novel critical behaviors, distinct from their Hermitian counterparts, and in some cases, surprisingly resilient or even enhanced. We discuss the role of exceptional points as hallmarks of non-Hermitian systems, their influence on energy spectra, and their implications for criticality and topological invariants. Furthermore, we examine the methodologies for defining observables and statistical ensembles in these non-Hermitian settings, emphasizing the distinctions and occasional controversies that arise. The findings provide critical insights into the fundamental principles governing quantum criticality in dissipative environments and pave new avenues for engineering and understanding open quantum technologies, from quantum sensing to robust quantum information processing.
An exceptional point (EP) is exclusive for non-Hermitian systems and distinct from that at a degeneracy point (DP), supporting intriguing dynamics which can be utilized to probe quantum phase transitions and prepare eigenstates in a Hermitian many-body system. In this paper, we investigate the transition from a DP for a Hermitian system to an EP driven by non-Hermitian terms. We present a theorem on the existence of a transition between a DP and EP for a general system. Specifically, one of twofold degenerate eigenstates of a Hermitian system becomes a coalescing state when a selected non-Hermitian term is added. The obtained EP is robust to the strength of non-Hermitian terms. We illustrate the theorem by an exactly solvable quasi-one-dimensional model, which allows for the existence of a transition between fully degenerate and exceptional spectra driven by non-Hermitian tunnelings in real and k spaces, respectively. We also study the EP dynamics for generating coalescing edge modes in Su-Schrieffer-Heeger-like models. This finding reveals the ubiquitous connection between DPs and EPs.
The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.
Non-Hermitian physics exhibits unique physical properties beyond those of traditional Hermitian systems, such as symmetry breaking, the emergence of exceptional points, topological phase transitions, and more. These phenomena have been extensively studied across various platforms, including quantum optics, cold atom systems, superconducting circuits, and condensed matter physics. Rydberg atoms, with their long-range interactions and flexible controllability, provide a promising platform for the experimental realization of non-Hermitian physics. This review primarily summarizes the key experimental and theoretical achievements in the field of non-Hermitian physics within Rydberg atomic systems in recent years. It outlines the fundamental construction of non-Hermitian Hamiltonians, reveals the effective dissipation mechanisms induced by Rydberg atomic interactions, and discusses their impact on spectral properties and symmetry breaking. These studies not only deepen the understanding of quantum phase transitions in non-Hermitian many-body systems but also highlight the unique value of Rydberg atomic platforms in realizing and controlling topological states.
The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.
Quantum matter emerges from the interplay of fluctuations, topology, and entanglement, which - in equilibrium - governs quantized transport, universal criticality, and topological classification. Non-Hermitian systems, widely explored in platforms ranging from electric circuits to photonics, are intrinsically out-of-equilibrium, and display fundamentally new phenomena, including complex spectra, spectral winding, exceptional topology, and non-unitary dynamics. A central challenge is understanding how the complex single-particle spectrum governs universal many-body behavior. We introduce a symmetry-protected dynamical topological index derived directly from the complex spectrum. Through the lens of algebraic topology, more specifically Morse theory, we identify critical points in the spectrum with topological defects, whose curvature and stability are protected under continuous deformations. This links spectral geometry to many-body observables, unifying non-Hermitian band topology, entanglement, and transport. We demonstrate that non-Hermitian quantum criticality in non-interacting systems is controlled by gain-and-loss-selected non-equilibrium steady states, which dynamically generate an emergent imaginary Fermi surface whose Fermi points host scale-invariant gapless modes with logarithmic entanglement scaling and algebraic correlations. Our work establishes a unified framework for non-Hermitian quantum matter, connecting spectral topology to Morse theory, revealing a topological foundation of non-equilibrium quantum criticality.